But on the other hand, the devices may try to use entanglement to cheat and pass the protocol without producing additional randomness. We show that the monogamous nature of entanglement prevents this from happening.

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Next, this thesis studies the parallel repetition of games with entangled players. Raz's classical parallel repetition theorem SICOMP is an influential result in complexity theory showing that the maximum success probability of unentangled players in a two-player game must decrease exponentially when the game is repeated in parallel. Its proof is highly non-trivial, and a major open question is whether it extends to the case of entangled players.

We make progress on this question in several ways. First, we present an efficient transformation on games called "anchoring" that converts any k-player game G into a k-player game G[upside down upper case T] such that the entangled value of its n-fold parallel repetition, Gn[upside down upper case T], is exponentially small in n provided that the entangled value of G is less than 1.

## Quantum Entanglement of Complex Structures of Photons | Robert Fickler | Springer

Furthermore, the transformation is completeness preserving, in that if the entangled value of G is 1, then the entangled value of Gn[upside down upper case T] is also 1. This yields the first gap amplification procedure for general entangled games that achieves exponential decay. We also show that parallel repetition of a game causes the entangled value to decrease at a polynomial rate with the number of repetitions.

In particular, this gives the first proof that the entangled value of a parallel repeated game converges to 0 for all games who entangled value is less than 1. The third result of this thesis on entangled parallel repetition is an improved analysis of the parallel repetition of free games with entangled players. Free games are those where the players' questions are independent of each other.

In contrast, the best parallel repetition theorem for free games with unentangled players, due to Barak, et al. This suggests a separation between the behavior of entangled games and unentangled games under parallel repetition. In the final part of this thesis, we examine message authentication in a quantum world. Message authentication is a fundamental task in cryptography that ensures data integrity when communicating over an insecure channel.

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- [] PhD thesis: Multipartite entanglement and quantum algorithms.
- Introduction;

We consider two settings. Currently, another outstanding revolution is taking place in a crossroad where information science meets quantum mechanics this being the quantum information field. Such an area of work contemplates both the fascinating theoretical aspect of quantum correlations, as well as implementations towards quantum tasks performed by a universal quantum computer; tasks that cannot be realised or they are hard to implement within the classical domain.

This Thesis is devoted to study the dynamics of quantum entanglement in spin-optomechanics systems.

In particular, we explore the quantum stabilization of quantum entanglement, a quantum concentration scheme in opto-mechanics and an interfacing of matter and light towards quantum networking applications. Additionally, we also investigate theoretical aspects of quantum correlations within thermal environments, as well as the topical area of quantum sudden transitions. In Chapter 1, we provide a brief summary of quantum information and of the quantum optics framework to cover elementary concepts and techniques used subsequently in this work.

Subsequently, in Chapter 2 we present the stabilization of quantum entanglement in a non-linear qubit-oscillator system. The inclusion of a modest nonlinearity gives three results, i the loss of periodicity of the system, ii the occurrence of quadrature squeezing appearing for a short time, and iii the quantum entanglement reaches higher values in contrast to the case without non-linearity.

Here, one of the optical modes is injected into a cavity at first, and thereafter, it is nonlinearly coupled to a mechanical oscillator.

## Quantum Entanglement Confirmed With Light From Distant Quasars

Afterwards, the position of the oscillator is measured using pulsed optomechanics and homodyne detection. She is currently a postdoctoral associate and a research fellow of the Swiss National Science Foundation at Harvard University. Here, she develops on-chip optical devices for the manipulation of light and its use in fundamental sciences and industry. She is involved in mentoring work and outreach activities at the faculty and university level.

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Fabian Langer was born on the 17th of March in Bamberg, Germany. Here, he learned about ultrafast quantum physics of condensed matter systems and started to work on lightwave electronics. Fabian Langer received his PhD in March Achim Woessner ICFO, The Institute of Photonic Sciences, Castelldefels Barcelona , Spain for graphene plasmons detected electrically and used to build ultra-compact modulators for the first time enabling applications in biosensing and mid-infrared integrated optics.

Maiken H. Fernando G.